Critical Reasoning – The Statistics Question 2

In the previous post on Critical Reasoning we looked at the method of tackling statistics-based CR questions on the GMAT®. Let us look at another statistics-based questions to reinforce our learning.

As discussed in the previous post, the answer to a statistics-based question will either be a statistic or an interpretation of the stat being discussed in the argument. More often than not, test-takers answer these questions incorrectly because they do not take time out to understand the stat being discussed. The GMAT® question below is the best example.

Between 1975 and 1985, nursing-home occupancy rates averaged 87 percent of capacity, while admission rates remained constant, at an average of 95 admissions per 1000 beds per year. Between 1985 and 1988, however, occupancy rates rose to an average of 92 percent of capacity, while admission rates declined to 81 per 1000 beds per year.

If the statements above are true, which of the following conclusions can be most properly drawn?

(A) The average length of time nursing-home residents stayed in nursing homes increased between 1985 and 1988.
(B) The proportion of older people living in nursing homes was greater in 1988 than in 1975.
(C) Nursing home admission rates tend to decline whenever occupancy rates rise.
(D) Nursing homes built prior to 1985 generally had fewer beds than did nursing homes built between 1985 and 1988.
(E) The more beds a nursing home has, the higher its occupancy rate is likely to be.

The key to answering this question correctly is understanding what occupancy rate and admission rate mean — occupancy rate is the percentage of beds that are occupied, while admission rate refers to the number of people who are admitted (for occupying beds) per 1000 beds. The situation is that while number of proportion of people getting admitted has gone down, the occupancy rate has gone up. The correct option should ideally, analyse and put both of these stats in perspective.

Option (C) seems to be best option but based on sample of just two data points it is not possible to conclude that whenever admission rates decline occupancy rates rise. The conclusion commits the fallacy of hasty generalization.

An analogous example might make the situation clearer — a survey that asked people whether they had a bottle of jam at home, showed that in the last decade the number of families per 100 families that answered “yes” increased from 6 to 8 but during the same decade, sales of jam fell by 20%. Can you guess how this could have happened?

The only way this can happen is that people are not really consuming a lot of jam and even when they are purchasing it, they are consuming it very slowly hence the jam is staying in the fridge for longer.

Even in this question the situation is similar, while admission rates have gone down, people who are admitted are staying for a longer time! Only option (A) states this.

Overtly statistics-based Critical Reasoning questions like these are perhaps the few GMAT® CR questions where you can arrive at the correct answer without even looking at the answer options, provided you take time out to understand the statistic in question!

There is another type of statistics question, one that is more covert and well disguised because it barely uses any numbers.

The key to identify this type of question is to check whether the argument is built around a metric even though there no numbers are mentioned, for example, rate of disease or percentage of people contacting a virus etc.; basically anything involving a percentage or a fraction or proportion.

In all such questions evaluate answer options with respect to their impact on the percentage, fraction or proportion:
• How does this option change the numerator?
• How does it impact the denominator?

By identifying and approaching statistics questions from a purely data analysis perspective and not from a Verbal Ability perspective, you will see an increase in your accuracy and a decrease in the average time taken to solve CR questions.